Interdependent Total Factor Productivity in an Input-Output model

Abstract

Industries learn productivity improvements from their suppliers. The observed empirical importance of these interactions, often omitted by input-output models, mandates larger attention. This article embeds interdependent total factor productivity (TFP) growth into a general non-parametric input-output model. TFP growth is assumed to be Cobb-Douglas in TFP-stocks of adjacent sectors, where elasticities are the input-output coefficients. Studying how the steady state of the system reacts to changes in research effort bears insight for policy and the input-output literature. First, industries higher in the supply chain see a greater multiplication of their productivity gains. Second, the presence of `laggard' industries can bottleneck the the rest of the economy. By deriving these insights formally, we review a canonical method for aggregating TFP -- Hulten's Theorem -- and show the potential importance of backward linkages.